The Senate has dealt another $2bn blow to the government’s budget – by refusing to pass legislation that repeals personal income tax cuts legislated by the former government but then deferred.

It remains on track to repeal the carbon tax by Thursday, but the government is struggling with the new Senate. Earlier on Wednesday the government was confidently predicting it had the Senate numbers to “gag” debate and force an immediate vote on all the repeal bills – only to lose the gag motion when three crossbench senators voted against it.

Labor, the Greens, the three Palmer United party (PUP) senators, independent senator Nick Xenophon, Family First senator Bob Day and Liberal Democrat senator David Leyonhjelm and Motoring Enthusiast Ricky Muir voted against a second reading of the bill repealing personal income tax cuts that had been promised by the then Labor government and then deferred in its last budget.

The finance minister, Mathias Cormann, said the vote meant Labor "voted against their own decision in their final budget to defer the second round of personal tax cuts linked to the carbon tax".

"It is clear that Labor is in denial about the state of the budget and the imminent repeal of the carbon tax. When the carbon tax is gone, there will be no need to provide additional compensation for a tax that will not exist," Cormann said.

The former government pocketed $1.5bn in budget savings from the deferral, but never legislated it. The cuts cost about $700m a year and the start date means the current four-year forward estimates would include three years of that cost – leaving a shortfall closer to $2bn. The Senate vote means the tax cuts remain in law, due to come into effect on 1 July, 2015.

The legislated tax changes from 1 July, 2015, provide for an annual tax cut of $228 for taxpayers with a taxable income of between $22,000 and $37,000, with the benefit declining after this income threshold to $13 for taxpayers with a taxable income of more than $80,000.

The tax cut comes from an increase in the tax-free threshold, from $18,200 to $19,400.

Introducing the carbon tax repeal bills last year, Joe Hockey explained the government’s decision to legislate to repeal the tax cuts in this way.

“In its final budget handed down on 14 May, 2013, the former government deferred the 2015 personal income tax cuts and booked a $1.5bn saving over the forward estimates. But the former government never followed through by legislating this change,” the treasurer said.

“The government understands households will continue to face cost-of-living pressures. That is why we will keep the current personal income tax thresholds and the fortnightly pension and benefit increases. But with the repeal of the carbon tax, there is no longer any need for the second round of personal income tax cuts.”

Leyonhjelm forced the tax cut bills to be voted on separately from the rest of the carbon tax repeal package because he would not vote to repeal tax cuts.

The government’s “gag” motion was opposed by Labor, the Greens and senators Xenophon, Madigan and Muir. It was supported by the PUP senators.

“In an attempt to ambush the Senate, the government moved to have the bills declared urgent so it could guillotine debate and force them through by lunchtime today. This move fell flat when key crossbench senators stood up to government pressure and upheld the Senate’s democratic role in scrutinising and debating legislation,” Wong said.

“Mr Abbott’s office briefed the media that the bills would be passed by lunchtime and that the prime minister would fly into Canberra tomorrow for a triumphant media conference.”